IMO you need to have a larger seating area all one material. I need to see a to scale drawing of the whole space and with all measurements clearly marked and some pictures showing the space and how it relates to the house. That fence is aeysore at least power wash it for sure . Is this a condo unit or a stand alone home? Do you have rules about fencing with HOA ?

following

It would not be an 'outdoor oasis' for me unless it was filled with plants! Since it is such a confined space and you have so many requirements for it, I think you will need to prioritize what is essential and what is not.

I recently completed streaming a series from Gardeners' World that focused on tiny garden spaces. These are extremely common in the UK where this series originates and it was inspiring to see what creative gardeners could do in a very confined space. 6 meters square (about 400 sf) was the maximum garden size.

Tiny backyard garden designs

I think landscaping is the main thing. For an easy fix to make it nice for the summer, you could place some plants around the fence.

This is going to be a multi-year project that will likely require more money than you're currently willing to spend, so I'd do it in stages.

Create flower/planting beds around the perimeter of the fence. You can either do this with a series of rectangular planters you build yourself out of railroad ties or similar, or dig out beds from the grass. Plant flowering shrubs, Japanese maples, and perhaps some perennial climbing vines like roses or clematis to soften the fence. (And yes, agree the fence needs cleaning, as Patricia suggests above.)

For the patio area, I think I'd cover the concrete with stone pavers. Create two separate areas, one for eating and one for lounging/conversation. You could eventually add a pergola over the patio for shade. Some inspiration:

Beautiful Backyards · More Info

Retaining Wall and Planter Box Project San Ramon · More Info

Josephine Remodel · More Info

Not a Pro,

@Design Interior South WOW! now that is great free design direction and in 15 steps!

Love it!!!

Please post updates as you go along updating your yard. I would love to see the outcome.

Please post a schematic diagram, do you have electric or would everything need to be solar?